D.1 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.
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D.1 Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.13, and 9.8 liters. Use α 0.01 level of significance and assume that the distribution of contents is normal.
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- For mated pairs of gallinules (type of water bird), let X equal the weight in grams of the male and Y the weight in grams of the female. Assume that X and Y have a bivariate normal distribution with #x = 415, o = 611, y = 347 and o=689. The correlation coefficient between X and Y is p = -0.25. (b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x. (d) Find E(Y|X = z) and Var(Y|X = x).Test the hypothesis that the average content of containers of a particular lubricant is 10 L if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume the distribution of contents is normal.The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a=0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.4 8.2 8.8 12.6 13.1 6.1 9.90 11.3 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and H₂? Ο Α. Ho: με 11.0 H₂>11.0 O D. Ho: 11.0 H: ≤11.0 A O A. Fail to reject Ho because the P-value is greater than the significance level. OB. Reject H, because the P-value is greater than the significance level. OC. Reject Ho because the P-value is less than the significance level. OD. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A.…
- A population of values has a normal distribution with μ=248.4μ=248.4 and σ=23.6σ=23.6. You intend to draw a random sample of size n=32n=32.Find P18, which is the score separating the bottom 18% scores from the top 82% scores.P18 (for single values) = Find P18, which is the mean separating the bottom 18% means from the top 82% means.P18 (for sample means) = Enter your answers as numbers accurate to 1 decimal place.************NOTE************ round your answer to ONE digit after the decimal point! ***********Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.A population of values has a normal distribution with μ=153.9μ=153.9 and σ=82.9σ=82.9. You intend to draw a random sample of size n=115n=115.A) Find P86, which is the score separating the bottom 86% scores from the top 14% scores. P86 (for single values) = B) Find P86, which is the mean separating the bottom 86% means from the top 14% means. P86 (for sample means) =Suppose, household color TVs are replaced at an average age of μ = 9.0 years after purchase, and the (95% of data) range was from 5.8 to 12.2 years. Thus, the range was 12.2 − 5.8 = 6.4 years. Let x be the age (in years) at which a color TV is replaced. Assume that x has a distribution that is approximately normal. (a) The empirical rule indicates that for a symmetric and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviationFor a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value − low value 4 where it is estimated that about 95% of the commonly occurring data…
- Some frozen food dinners were randomly selected from this week's production and destroyed in order to measure their actual calorie content. The claimed calorie content is 200. Here are the calorie counts for each frozen dinner selected: 193 213 193 211 202 192 208 204 186 199 199 186 Assume the distribution of calories is normal. (a) The test statistic (z/t) is ☐. Use two decimals. (b) Does the sample indicate that the mean calorie content is 200? Set a = (c) Find the P-value of the test in (a)-(b). = 0.01. ?A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 215 225 235 240 255 260 225 Total Blood Cholesterol (After) 214 222 240 237 254 257 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μd=μ1−μ2. Choose the correct…An employment information service claims the mean annual salary for senior level product engineers is $95,000. The annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At α=0.05, test the claim that the mean salary is $95,000. Complete parts (a) through (e) below. Assume the population is normally distributed. Annual Salaries: 100,683 96,363 93,511 112,615 82,435 74,211 77,041 80,894 102,398 76,130 104,053 104,040 91,094 82,028 85,015110,258 Identify the claim and state H0 and Ha. H0:___ ___ ____ Ha: ___ ___ ____ (Type integers or decimals. Do not round.) The claim is the________(alternative or null) hypothesis. Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t0= ____ , _____ (Use a comma to separate answers as needed. Round to two decimal places as needed.) The standardized test statistic is T=_______________________________…
- Women are recommended to consume 1790 calories per day. You suspect that the average calorie intake is smaller for women at your college. The data for the 15 women who participated in the study is shown below: 1959, 1908, 1789, 1544, 1805, 1656, 1899, 1811, 1686, 1688, 1687, 1943, 1612, 1789, 1467 Assuming that the distribution is normal, what can be concluded at the α = 0.05 level of significance? For this study, we should use The null and alternative hypotheses would be: H0: H1: The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly less than 1790 at α = 0.05, so there is sufficient evidence to conclude that the population mean calorie intake for women at your college is equal to 1790. The data suggest the populaton…Use the following sample to evaluate H0: μ = 65, at significance level α = 0.05. 53 75 68 53 57 12 4 10 45 94 23 73 9 41 79 92 90 46 49 71 State the correct test and your conclusion. T-test. Reject Ho. T-test. Fail to reject Ho. Z-test. Fail to reject Ho. Z-test. Reject Ho.Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 8.00 ml/kg for the distribution of blood plasma. When finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) Z=0.005 (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) the distribution of volumes is normal ✔ is known o is unknown the distribution of volumes is…